Well, I am thinking of courage in more general terms. Certainly it takes courage to face a vastly superior foe, but it also takes courage to admit to someone that you're wrong and ask for their forgiveness.
Perhaps TW isn't as... momentous as HP is with regards to good versus evil events. But in what we do see, such as the fight in EC, Edward fights not against insurmountable odds, but against opponents he believes he can best. That doesn't really take any courage to do. Even in the confrontation of BD, while it can be thought that speaking up to the Volturi took courage, it was something he'd accepted he'd have to do (and Bella kinda ruined it with her whole "I'm so awesome!" routine but that's another topic).
Compare this with say, Alice, who left everyone in the middle of BD to go find something she didn't even know existed. Now that took courage- facing the unknown (especially for her, who is so used to seeing what could be) and having to believe that her family would be fine without her (and Jasper).